Further heavy snow has been forecast for high ground in Wales. Photograph: Dan Kitwood/Getty Images

The cold snap returned to Britain today – just in time to disrupt the country's return to work after the Christmas break.

Train services were disrupted at Glasgow, Inverness airport was forced to close and roads across the country saw black ice cause accidents.

Up to 30cm (12in) of snow fell today on high ground in Wales, prompting warnings to inexperienced hikers venturing on to the mountains of Snowdonia or the Brecon Beacons.

Snow showers also hit parts of the West Country, the Midlands – up to Dorridge and neighbouring areas south of Birmingham – and parts of the north-east of England. Areas which were spared snow experienced heavy rain, particularly England's south-east.

Severe weather warnings were in place for large swaths of the middle of England, with the snow expected to ease in the early hours of the morning, said a Met Office spokesman. "After the snow a band of rain will push south on Wednesday and Thursday, clearing and giving brighter weather for the weekend," he said.

Stephen Davenport, a forecaster with MeteoGroup, said there was a distinct difference in temperatures throughout the UK. "You can virtually draw a line from Suffolk to the Bristol Channel and say that, south of that, there will be no snow," he said. "Temperatures may be as mild as 10C (50F) in the south-west of England tomorrow, but in other areas, such as Scotland, they will struggle to get above freezing."

More wintery weather is expected tomorrow with cold temperatures and fresh winds, and more snow likely to fall on higher ground, especially in Wales.

The Welsh assembly said it had stockpiles of salt and grit and a contingency plan to divert supplies from motorways if snow threatened to disrupt main roads.

Holiday engineering work was adding to the disruption caused by ice to rail services between Glasgow, Ayr, Largs, Ardrossan and Wemyss Bay.

On the roads, the A66 at Stockton-on-Tees, the A19 at Sunderland and the A42 in Leicestershire saw long delays caused by accidents.

Between midnight and 3pm today , the AA attended about 14,000 breakdowns. It expected the day's total to exceed 18,000, compared with about 8,500 on a normal Tuesday.

The busiest areas for AA patrol teams were the north of Scotland, south Wales and Gloucestershire. The AA said it had its busiest Christmas Day for 20 years.

The father of a man who went missing in freezing and snowy weather appealed today for his safe return. Adam Passfield failed to return home after an evening out with football club friends in Chelmsford, Essex, 10 days ago. The 22-year-old is described as about 6ft tall and of slim build with short, straight brown hair. His father, Kevin, said: "We can only hope the new year will bring good news."